{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/counting-parabolic-double-cosets-in-symmetric","title":"Counting Parabolic Double Cosets in Symmetric Groups","arxiv_id":"2010.13256","date":"2020-10-26","proceeding":null,"authors":["Thomas Browning"],"abstract":"Billey, Konvalinka, Petersen, Solfstra, and Tenner recently presented a method for counting parabolic double cosets in Coxeter groups, and used it to compute $p_n$, the number of parabolic double cosets in $S_n$, for $n\\leq13$. In this paper, we derive a new formula for $p_n$ and an efficient polynomial time algorithm for evaluating this formula. We use these results to compute $p_n$ for $n\\leq5000$ and to prove an asymptotic formula for $p_n$ that was conjectured by Billey et al.","url_abs":"https://arxiv.org/abs/2010.13256v2","url_pdf":"https://arxiv.org/pdf/2010.13256v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"counting-parabolic-double-cosets-in-symmetric","repo_url":"https://github.com/tb65536/ParabolicDoubleCosets","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}